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pix_strange_attractor [2007-06-20 18:14] – pixpix_strange_attractor [2008-04-10 15:20] (current) – 77.128.39.6
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 a place for my sketchy notes on the project... a place for my sketchy notes on the project...
  
 +more info
 +  * my initial research report: [[pix_research_report]]
 +  * which evolved into: [[research_report_pix]]
  
  
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 actually, looking closer at the demo code, the SpinButton demo displays the text manually with a text box. so making a custom controller should be easy. the spin button will still store integers internally, but i think i will take something of a fixed-point approach, and just specify a multiplier that is applied to the internal SpinButton  value to generate a fractional value. actually, looking closer at the demo code, the SpinButton demo displays the text manually with a text box. so making a custom controller should be easy. the spin button will still store integers internally, but i think i will take something of a fixed-point approach, and just specify a multiplier that is applied to the internal SpinButton  value to generate a fractional value.
- 
  
 ===== exploring the space ===== ===== exploring the space =====
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  * highf-100.png:  * highf-100.png:
 +
 +note from the future (!!): i realise now that this is actually a plot of the basin of attraction (i was changing the initial value for each point in the image, not the constants of the equation). this is also why the fractal dimension isn't changing very obviously. much much later, i do a plot of the fractal dimension when actually changing the constants and the results are more interesting.
  
  
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-as an aside i realised that different starting points is just the same as choosing different coefficients, since the effect of choosing a different starting point could also be achieved by shifting the graph by a constant offset, which can be achieved by changing the coefficients. +as an aside i realised that different starting points is just the same as choosing different coefficients, since the effect of choosing a different starting point could also be achieved by shifting the graph by a constant offset, which can be achieved by changing the coefficients. //wow, this is super-wrong. although this assumption kind of holds with a normal polynomial, if you start iterating, it all falls down.//
  
 ==== 17 Dec 2006 ==== ==== 17 Dec 2006 ====
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 so, to describe a bit more. the black and green areas are where the map doesn't just spin off to infinity, but keeps returning values. in the black areas, the fractal dimension is very low, so it is possible that the map just returns a small number of points over and over again. in the green areas, the fractal dimension is higher (and highest where the green is lightest). the points with highest dimension probably produce points in a voluminous cloud, or at best a sheet. the darker green areas possibly producing points arranged as lines. so, to describe a bit more. the black and green areas are where the map doesn't just spin off to infinity, but keeps returning values. in the black areas, the fractal dimension is very low, so it is possible that the map just returns a small number of points over and over again. in the green areas, the fractal dimension is higher (and highest where the green is lightest). the points with highest dimension probably produce points in a voluminous cloud, or at best a sheet. the darker green areas possibly producing points arranged as lines.
  
-it would be really interesting to be able to click around on this image and see the attractor that each point represents. i' not sure yet if that will make it into the research or if it will be a future direction.+it would be really interesting to be able to click around on this image and see the attractor that each point represents. i'm not sure yet if that will make it into the research or if it will just be listed as a future direction. 
 + 
 +=== Yet another animation === 
 + 
 +Oh, and there is this neat new animation. First some ramblings. I was showing the parameter plots above to Tim Boykett, and he pointed out an important assumption that I was making. The plots are specifically plotting the presence of attractors that just happen to have 0,0,0 in their basin of attraction (because the function doing the escape-plot always uses 0,0,0 as the starting point). To investigate how important this assumption was, I made an animation of parameter plots for changing initial values. The base attractor is the one used in all of the images called "highf" above. At the start of the animation, the initial value used for the parameter plots is -1,0,0, and by the end it is 1,0,0. In the middle of the animation, you should see a frame that looks like highf-c00-01-512esc20.png above (only with the black part filled in white, and rotated 90 degrees counter-clockwise - the renderer has changed a bit) when the initial value hits 0,0,0. 
 + 
 +[[http://lib.fo.am/_media/movingbasin.gif|{{movingbasin.gif?64x64|click for full size}}]] 
 + 
 +{{movingbasin.gif?64x64|click for full size}} 
 + 
 +(this is here twice because the second one, which is the //right way// to link images with thumbnails, results in a slightly corrupted animation)
  
 ==== twiki era cruft ==== ==== twiki era cruft ====
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